Visualization of semileptonic form factors from lattice QCD

TL;DR

This paper proposes a method to visualize lattice-QCD semileptonic form factors as curves with error bands, incorporating correlations from fits to better compare with experimental data.

Contribution

It introduces a visualization approach that displays lattice-QCD results as curves with error bands, accounting for correlations in both statistical and systematic errors.

Findings

Demonstrates the method with D -> pi l nu and D -> K l nu form factors

Uses analyticity-based fit for B -> pi l nu form factor

Addresses correlations in systematic and statistical errors

Abstract

Comparisons of lattice-QCD calculations of semileptonic form factors with experimental measurements often display two sets of points, one each for lattice QCD and experiment. Here we propose to display the output of a lattice-QCD analysis as a curve and error band. This is justified, because lattice-QCD results rely in part on fitting, both for the chiral extrapolation and to extend lattice-QCD data over the full physically allowed kinematic domain. To display an error band, correlations in the fit parameters must be taken into account. For the statistical error, the correlation comes from the fit. To illustrate how to address correlations in the systematic errors, we use the Becirevic-Kaidalov parametrization of the D -> pi l nu and D -> K l nu form factors, and a analyticity-based fit for the B -> pi l nu form factor f_+.